File:Pendulum with rotating pivot.gif
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Pendulum_with_rotating_pivot.gif (440 × 440 pixels, file size: 9.01 MB, MIME type: image/gif, looped, 500 frames, 50 s)
Captions
Captions
Simple pendulum with pivot attached to a disk that rotates faster and faster.
Summary[edit]
| Description |
English: Simple pendulum with pivot attached to a disk that rotates faster and faster. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1260248598312255493 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code[edit]
l = 1;
pivot[t_] := {Sin[0.06 t^2], -Cos[0.06 t^2]};
x[t_] := pivot[t][[1]] + l Sin[\[Theta][t]]
y[t_] := pivot[t][[2]] + l Cos[\[Theta][t]]
T[t_] := FullSimplify[m/2 (D[x[t], t]^2 + D[y[t], t]^2)]
V[t_] := m g y[t]
L = T[t] - V[t];
eq\[Theta] = D[D[L, \[Theta]'[t]], t] - D[L, \[Theta][t]]
m = 1; g = 1;
sol = NDSolve[{eq\[Theta] == 0, \[Theta][0] == \[Pi], \[Theta]'[0] == 0}, \[Theta][t], {t, 0, 100}]
m =.; g =.;
p1 = Table[
Show[
Graphics[{
LightGray, Disk[{0, 0}, 1], White, Line[{-pivot[\[Tau]max], pivot[\[Tau]max]}],
Line[{{-pivot[\[Tau]max][[2]], pivot[\[Tau]max][[1]]}, {pivot[\[Tau]max][[2]], -pivot[\[Tau]max][[1]]}}]
}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}],
ParametricPlot[
Evaluate[{x[t], y[t]} /. sol][[1]] /. {t -> \[Tau]}, {\[Tau], Max[0, \[Tau]max - 1], \[Tau]max}, PlotStyle -> {Thick, Orange}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, Axes -> False]
,
ParametricPlot[
Evaluate[{x[t], y[t]} /. sol][[1]] /. {t -> \[Tau]}, {\[Tau], 0, \[Tau]max}, PlotStyle -> {Thick, Orange, Opacity[0.3]}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}, Axes -> False]
,
Graphics[{
Black, Thick, Line[{pivot[\[Tau]max], Evaluate[{x[t], y[t]} /. sol][[1]] /. {t -> \[Tau]max}}], Disk[Evaluate[{x[t], y[t]} /. sol][[1]] /. {t -> \[Tau]max}, 0.1], Disk[pivot[\[Tau]max], 0.04],
Orange, Disk[Evaluate[{x[t], y[t]} /. sol][[1]] /. {t -> \[Tau]max}, 0.08]
}, PlotRange -> {{-2.5, 2.5}, {-2.5, 2.5}}]
]
, {\[Tau]max, 0.01, 50, 0.1}];
ListAnimate[p1]
Licensing[edit]
I, the copyright holder of this work, hereby publish it under the following license:
 
|
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
|
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 16:28, 16 December 2020 | | 440 × 440 (9.01 MB) | Jahobr (talk | contribs) | Trying to get the file under the 100 MPx limit. |
| 16:22, 16 December 2020 |  | 440 × 440 (30 KB) | Jahobr (talk | contribs) | Cropped 8 % horizontally, 8 % vertically using CropTool with lossless mode. Trying to get the file under the 100 MPx Limit. | |
| 12:18, 13 May 2020 |  | 480 × 480 (9.15 MB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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